In this paper we obtain the criterion of weak convergence of the sequence of the sum of the first $n$ terms of the linear process $\left\{X_{kn} ,\; k=1,2,...,n;\; n=1,2,...\right\}$ with random coefficients $\left\{v^{k} ,k\in {\mathbb N}\right\}$, generated by the innovation sequence $\left\{\xi _{kn} ,k\in Z\right\}$ satisfying the condition of infinite smallness to the limit distribution and as a consequence of this result we obtain the analog of the Lindeberg-Feller theorem for the auto regression process with random parameter $v,\; 0{\rm \; }<{\rm \; }v<1$. In addition, the strong law of large numbers and the law of iterated logarithm are proved.
| Mualliflar | T.M.Zuparov, A.I.Jovliev |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashriyot | Ўзбекистон Республикаси ФА Математика институти |
| ISSN | 2010-7269 |
| Nashr sanasi | 2025-09-06 |
| Jild | 69 |
| Son | 3 |
| Betlar | 176-180 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.29229/uzmj.2025-3-19 |
| Indeksga qo‘shilgan | 2026-08-26 |
DOI: 10.29229/uzmj.2025-3-19 · Maqolaning asl sahifasi
Auto regression process, linear process, central limit theorem, strong law of large numbers, law of iterated logarithm
| APA | T.M.Zuparov, & A.I.Jovliev (2025). Limit theorems for auto regression processwith random parameter v, 0 < v < 1. O‘zbekiston matematika jurnali, 69(3), 176-180. https://doi.org/10.29229/uzmj.2025-3-19 |
|---|---|
| GOST (OAK) | T.M.Zuparov, A.I.Jovliev Limit theorems for auto regression processwith random parameter v, 0 < v < 1 // O‘zbekiston matematika jurnali. – 2025. – T. 69, № 3. – P. 176-180. – DOI: 10.29229/uzmj.2025-3-19. |
| MLA | T.M.Zuparov, and A.I.Jovliev. “Limit theorems for auto regression processwith random parameter v, 0 < v < 1.” O‘zbekiston matematika jurnali, 69(3), 176-180, 2025. https://doi.org/10.29229/uzmj.2025-3-19 |
| Chicago | T.M.Zuparov, and A.I.Jovliev. “Limit theorems for auto regression processwith random parameter v, 0 < v < 1.” O‘zbekiston matematika jurnali, 69(3), 176-180 (2025). https://doi.org/10.29229/uzmj.2025-3-19 |
| Harvard | T.M.Zuparov, and A.I.Jovliev (2025) ‘Limit theorems for auto regression processwith random parameter v, 0 < v < 1’, O‘zbekiston matematika jurnali, 69(3), 176-180. https://doi.org/10.29229/uzmj.2025-3-19 |
| BibTeX | @article{tmzuparov2025,
title = {Limit theorems for auto regression processwith random parameter v, 0 < v < 1},
author = {T.M.Zuparov and A.I.Jovliev},
journal = {O‘zbekiston matematika jurnali},
year = {2025},
volume = {69},
number = {3},
pages = {176-180},
doi = {10.29229/uzmj.2025-3-19},
url = {https://doi.org/10.29229/uzmj.2025-3-19}
} |
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